As a silencing apparatus for a vehicle, there is a muffler located in an exhaust system of an internal combustion engine. The muffler installed under the floor of a vehicle has a flat cross-sectional shape such as an ellipse or a long circle, the width of which is greater than its height, so that the muffler is easily assembled to the vehicle.
A muffler of a flattened cross-sectional shape having a width W as shown in FIG. 11(a) will be discussed. According to such a muffler, air column resonance, in which both ends of the muffler in its width direction are closed, is generated in the width direction, and silencing performance of the muffler is deteriorated. A wavelength λ of a stationary wave that generates air column resonance in the width direction of the muffler is 2W/n (n: integer not less than 1). If sound velocity is defined as “C (C≈20×√{square root over ( )}T, T: gas temperature in muffler)”, the frequency f of the air column resonance is C×m/2W (m: integer not less than 1). Of the air column resonance, ones that appear most outstandingly are two stationary waves, i.e., a stationary wave (λ=2W) in which the wavelength λ is twice the muffler width as shown in FIG. 11(b), and a stationary wave (λ=W) in which the wavelength λ is equal to the muffler width as shown in FIG. 11(c).
Conventionally, as countermeasures against high frequency exhaust sound such as the air column resonance in the width direction of the muffler, a sub-muffler, which has a high frequency resonance structure and into which a sound absorbing material is charged, is installed in an exhaust system as shown in Patent Document 1.